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18 Cards in this Set
- Front
- Back
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The cordinate axes are ________, meaning that between any two s cordinates that might be specified, another x cordinate can be specified.
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CONTINUOS
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A sphere is 3-dimensional because three ______ cordinates are required to locate any point in the sphere.
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INDEPENDENT
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All road trips can be described as some up and down, left and right, forward and backward _______.
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MOTION
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Because you are not free to leave the surface of the earth, you can only experience motion in ________-___________ space, but you are also limited in how you travel in that space.
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THREE-DIMENSIONAL
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The concept of ______ can be used to describe the number of variables in required to define some system's trajectory.
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DIMENSION
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All of the definitions of dimensions have in common that the number of dimensions says something about the ________ of the system.
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COMPLEXITY
SMALL DIMENSIONAL SYSTEMS ARE LESS COMPLEX THAN LARGER DIMENSIONL SYSTEMS. |
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If we go beyond out discussion of positions on the surfae of the earth, we can apply the concept of dimension to systems that evolve in _____ but do not require normal space.
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TIME
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A ___, which is described as a sequence of infitinite number of points, has a dimension of 1.
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LINE
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The similarity dimension does not refer to ________ size or displacement in 3-dimensional space, but to strucure.
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ABSOLUTE
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_______ ___________ models provide a convenient technique for exploring signal propogation, causality and self-organization.
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CELLULAR AUTOMATA
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A cellular automation model is a collection of cells where the ____ characterisitc of each cell is determined by ____ characteristics of the cell and its neighbors, according to some simple set of rules.
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FUTURE, PRESENT
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The fractal dimension of the even-seventh cantor set is GREATER than the fractal dimension of the even-thirteenth st.
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FALSE
THE EVEN SEVENTH IS LESS THAN THE EVEN THIRTEENTH SET |
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The fractal dimension of a sieprenski carpet may be greater than 3.
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FALSE, NO MATTER WHAT THE FRACTAL DIMENSION (LOG N/LOG S) WILL ALWAYS BE THE SAME
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The dimension of any path that you would take to southern illinois would have a dimension b/t 2 and 3.
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FALSE, NOTHING IS MORE THAN 1, THAT APPROACHES INFINITE
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The correlation dimension is like the ....
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BOX COUNTING DIMENSION
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We use the box counting dimension for...
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PERIMETERS, ISLANDS, STOCK MARKET
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Some examples of similarity dimensions are...
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CANTOR SET, SIERPINSKI CARPYER
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The theoretical correlation dimension of a set of uniformly spaced points on a plane is
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2
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